TV Linear¶

Time-varying linear vehicle dynamics.

Notes

Defines a linear time-varying dynamics model with matrices A and B, registered via ModelSpec for integration with the optimization stack.

Param ¶

Parameters for the time-varying linear model.

Attributes:

Name	Type	Description
`A`	`Array`	State/control matrix of shape `(STATE_DIM, STATE_DIM + CONTROL_DIM)`.
`B`	`Array`	Bias term of shape `(STATE_DIM,)`.
`timestep`	`float`	Physics integration timestep.
`timestep_ratio`	`int`	Simulation steps per control step (static field).

vehicle_dynamics_tv_linear(x_and_u, params)

Evaluate the time-varying linear dynamics.

Parameters:

Name	Type	Description	Default
`x_and_u`	`Array`	Vehicle state-control vector of shape `(STATE_DIM + CONTROL_DIM,)`: x0: x position (global) x1: y position (global) x2: steering angle of front wheels x3: velocity in x direction x4: yaw angle u0: steering angle velocity of front wheels u1: longitudinal acceleration	required
`params`	`Param`	Parameter dataclass containing the linear map `A` and offset `B`.	required

Returns:

Type	Description
`Array`	Time derivative of the state-control vector, shape `(STATE_DIM + CONTROL_DIM,)`.

yaw_normalized_loss(output_states, target_states)

Yaw-normalized loss between output and target states.

Handles angular differences by wrapping them to [-pi, pi] and uses L1 loss for non-angular components.

Parameters:

Name	Type	Description	Default
`output_states`	`Array`	Predicted states of shape `(..., 5)`.	required
`target_states`	`Array`	Target states of shape `(..., 5)`.	required

Returns:

Type	Description
`float`	Total loss summed over all elements.

yaw_normalized_loss_per_element(
    output_states, target_states
)

Yaw-normalized loss per state dimension.

Parameters:

Name	Type	Description	Default
`output_states`	`Array`	Predicted states of shape `(B, T, 5)`.	required
`target_states`	`Array`	Target states of shape `(B, T, 5)`.	required

Returns:

Type	Description
`Array`	Loss per dimension of shape `(B, 5)`.

yaw_normalized_loss_per_item(output_states, target_states)

Yaw-normalized loss per item in the batch.

Assumes input shape is (B, T, D) where D=5.

Parameters:

Name	Type	Description	Default
`output_states`	`Array`	Predicted states of shape `(B, T, 5)`.	required
`target_states`	`Array`	Target states of shape `(B, T, 5)`.	required

Returns:

Type	Description
`Array`	Loss per batch item of shape `(B,)`.

yaw_normalized_loss_weighted(
    output_states, target_states, weights=None
)

Weighted yaw-normalized loss for state dimensions.

Parameters:

Name	Type	Description	Default
`output_states`	`Array`	Predicted states of shape `(..., 5)`.	required
`target_states`	`Array`	Target states of shape `(..., 5)`.	required
`weights`	`Array`	Per-dimension weights of shape `(5,)`. Defaults to ones.	`None`

Returns:

Type	Description
`float`	Weighted loss value.

Raises:

Type	Description
`ValueError`	If `weights` has an unexpected shape.